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Find the adjoint of the following matr...

Find the adjoint of the following matrices: `[(cosalpha,sinalpha),(sinalpha,cosalpha)]` (ii) `[(1,tanalpha//2),(-tanalpha//2, 1)]` Verify that `(a d j\ A)A=|A|I=A(a d j\ A)` for the above matrices.

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RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. Let A be a non-singular matrix. Show that A^T A^(-1) is symmetric i...

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  2. Find the adjoint of the following matrices: [(-3, 5),( 2, 4)] Verif...

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  3. Find the adjoint of the following matrices: [(cosalpha,sinalpha),(si...

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  4. Compute the adjoint of each of the following matrices: [[1, 2, 2],[ ...

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  5. For the matrix A=[[1,-1, 1],[ 2 ,3, 0 ],[18 ,2 ,10]] , show that A(a d...

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  6. If A=[[-4,-3,-3],[ 1, 0 ,1],[ 4 ,4, 3]] , show that a d j\ A=A .

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  7. If A=[(-1,-2,-2 ),(2, 1,-2),( 2,-2 ,1)] , show that a d j\ A=3A^T .

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  8. Find A(a d j\ A) for the matrix A=[[1,-2 ,3],[ 0, 2,-1],[-4 ,5, 2]] .

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  9. Find the inverse of the following matrix: |[costheta,sintheta],[-sinth...

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  10. Find the inverse of [(1, 2, 3),( 2, 3, 1),( 3, 1, 2)].

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  11. Find the inverse of [(1, 2, 5),( 1,-1,-1),( 2 ,3,-1)]

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  12. Find the inverse of [(2,-1, 1),(-1, 2,-1),( 1,-1, 2)]

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  13. Find the inverse of [(2, 0,-1),( 5, 1, 0),( 0, 1, 3)]

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  14. Find the inverse of [(0 ,1,-1),( 4,-3, 4),( 3,-3, 4)]

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  15. Find the inverse of [(0, 0,-1), (3 ,4 ,5),(-2,-4,-7)]

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  16. Find the inverse of [(1, 0, 0),( 0,cosalpha,sinalpha),(0,sinalpha,-cos...

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  17. Find the inverse following matrix and verify that A^(-1)A=I3 . [(1, ...

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  18. Find the inverse following matrix and verify that A^(-1)A=I3 . [(2, ...

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  19. For the following pair of matrix verify that (A B)^(-1)=B^(-1)A^(-1)...

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  20. For the following pair of matrix verify that (A B)^(-1)=B^(-1)A^(-1...

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